Newton-Kantorovich approximations under weak continuity conditions

DOI10.1007/s12190-010-0439-yzbMath1291.65166OpenAlexW2078923819MaRDI QIDQ2251742

Ioannis K. Argyros, Saïd Hilout

Publication date: 15 July 2014

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-010-0439-y

zbMATH Keywords

Newton's methodsemilocal convergenceBanach spacerecurrent functionsKantorovich-type majorants

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Convergence of the two-step combined method and uniqueness of the solution of nonlinear operator equations ⋮ Convergence analysis of the Gauss-Newton-Potra method for nonlinear least squares problems ⋮ On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions ⋮ A Newton-like method for generalized operator equations in Banach spaces ⋮ Some notes on split Newton iterative algorithm ⋮ Convergence of the Newton-Kurchatov method under weak conditions ⋮ Achieving an extended convergence analysis for the secant method under a restricted Hölder continuity condition

Uses Software

• NewtonLib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Improved generalized differentiability conditions for Newton-like methods
• General local convergence theory for a class of iterative processes and its applications to Newton's method
• A convergence theorem for Newton-like methods in Banach spaces
• On the Newton-Kantorovich hypothesis for solving equations
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• A semilocal convergence analysis for directional Newton methods
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• Convergence and Applications of Newton-type Iterations
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Convergence domains of certain iterative methods for solving nonlinear equations
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• New results on newton-kantorovich approximations with applications to nonlinear integral equations
• Generalized differentiability conditions for Newton's method
• A Unified Convergence Theory for a Class of Iterative Processes

This page was built for publication: Newton-Kantorovich approximations under weak continuity conditions